I am struggling with rotating coordinate systems in analytical mechanics. Consider a satellite orbiting the earth and attach a coordiate system to it such that

 

The coordinate orgin orbits the earth at the same radius and rotation rate W1 as the satellite and has its x axis radially outward and its y axis tangential in the direction of motion.

 

Now a 2nd satellite happens to be nearby and we want to express its motion relative to the 1st satellite. The equation of motion for this is

 

m a' = F - mAo - 2mW X v' - mW X W X r'

 

where F is the real force acting (gravity), Ao is the acceleration of the coord. origin (-W1*W1*R1) and -2mW X v' is the apparent Coriolis Force.

 

Which W (omega r/sec) goes in the formula for coriolis?

 

W of the orgin of the coordinate system or W of 2nd satellite?

 

Thanks,

Robert.

Sorry, my "rotating coordinate systems in analytical mechanics" is a bit rusty ( to the point of total oxidization ) but with only two options, could you not just test this mathematically?